Frequency-domain correlation: An asymptotically optimum approximation of quadratic likelihood ratio detectors

Wenyi Zhang, H. Vincent Poor, Zhi Quan

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

An approximate implementation is formulated and analyzed for the detection of wide-sense stationary Gaussian stochastic signals in white Gaussian noise. For scalar processes, the approximate detector can be realized as the correlation between the periodogram of the observations and an appropriately selected spectral mask, and thus is termed the frequency-domain correlation detector. Through the asymptotic properties of Toeplitz matrices, it is shown that, as the length of the observation interval grows without bound, the frequency-domain correlation detector and the optimum quadratic detector achieve identical asymptotic performance, characterized by the decay rate of the miss probability under the Neyman-Pearson criterion. The frequency-domain correlation detector is further extended to the detection of vector-valued wide-sense stationary Gaussian stochastic signals, and the asymptotic optimality of its performance is established through the asymptotic properties of block Hermitian Toeplitz matrices.

Original languageEnglish (US)
Pages (from-to)969-979
Number of pages11
JournalIEEE Transactions on Signal Processing
Volume58
Issue number3 PART 1
DOIs
StatePublished - Mar 1 2010

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering

Keywords

  • Block Toeplitz matrices
  • Error exponent
  • Frequency-domain correlation
  • Gaussian stochastic signal
  • Quadratic detection
  • Spectral mask

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